The pressureless damped Euler–Riesz equations

In this paper, we analyze the pressureless damped Euler-Riesz equations posed in either $\mathbb{R}^d$ or $\mathbb{T}^d$. We construct global-in-time existence and uniqueness of classical solutions for system around a constant background state. also establish large-time behaviors showing towards equilibrium as time goes to infinity. For whole space case, first show algebraic decay rate under additional assumptions on initial data compared theory. then refine argument have exponential convergence even space. case periodic domain, without any further regularity data, provide solutions.